Practice Questions
Concept Explanation
Population problems apply percentage increase/decrease to a base count. Always identify whether the change is on the original population or on a new value after prior change.
Increase and Decrease
New population = Original × (1 ± P/100).
Net Change Over Two Periods
Multiply successive multipliers. Example: +20% then −10% → 1.2 × 0.9 = 1.08 → net +8%.
Men and Women Split
If males are 55% of population, females are 45%. Use part-whole percentage relations carefully.
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Q1 EasyThe population of a town is 20,000. It increases by 15%. What is the new population?ExplanationIncrease = 3,000. New population = 20,000 + 3,000 = 23,000.
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Q2 EasyThe population of a village decreases from 12,000 to 10,800. What is the percentage decrease?ExplanationDecrease = 1,200. Percentage = (1,200/12,000) × 100 = 10%.
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Q3 EasyIn a city of 50,000 people, 60% are literate. How many are literate?Explanation60% of 50,000 = 30,000.
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Q4 EasyIn a survey, 35% of 4,000 respondents preferred product A. How many preferred product A?Explanation35% of 4,000 = 1,400.
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Q5 EasyThe population of a town decreases by 20% every decade. From 1,00,000, what is it after one decade?ExplanationNew = 1,00,000 × 0.8 = 80,000.
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Q6 EasyIn a town, 70% of adults are employed. If the adult population is 35,000, how many are employed?Explanation70% of 35,000 = 24,500.
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Q7 MediumThe present population of a town is 50,000. If the population of the town increased by 4% annually, then what will be the population after 2 years?ExplanationYear 1: 52,000. Year 2: 52,000 × 1.04 = 54,080. Or use successive formula: 4 + 4 + 16/100 = 8.16% on 50,000.
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Q8 MediumThe population of a town was 25,000. It increased by 12% and then decreased by 8%. The final population is:ExplanationFinal = 25,000 × 1.12 × 0.92 = 25,760.
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Q9 MediumA population of 80,000 grows by 10% in the first year and 5% in the second year. The population after two years is:ExplanationFinal = 80,000 × 1.1 × 1.05 = 92,400.
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Q10 MediumIn a colony, 45% of residents are children. If there are 1,800 children, what is the total population?Explanation45% of total = 1,800 → total = 1,800 × (100/45) = 4,000.
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Q11 MediumA city's population is 1,20,000. If males are 52% of the population, how many females are there?ExplanationFemales = 48% of 1,20,000 = 57,600.
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Q12 MediumA village population rises from 8,000 to 9,200. The percentage increase is:ExplanationIncrease = 1,200. Percentage = (1,200/8,000) × 100 = 15%.
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Q13 HardThe population of a village was 2,90,000. It increased by 10% in the first year and by 30% in the second year. Its population after two years is:ExplanationFinal = 2,90,000 × 1.1 × 1.3 = 4,14,700.
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Q14 HardAfter a 15% increase, a town has 46,000 people. What was the original population?ExplanationOriginal = 46,000/1.15 = 40,000.
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DS1 Easy
A town's population is about to change by a given percentage. What is the new population?
Statement IThe original population is 20,000.
Statement IIThe population increases by 15%.
ExplanationNew = 20,000 × 1.15 = 23,000. Statement I gives the base; Statement II gives the rate. Both are needed. -
DS2 Easy
A town undergoes successive percentage changes starting from 25,000. Is the final population more than 25,000?
Statement IAfter a 12% increase followed by an 8% decrease starting from 25,000, the final count is 25,760.
Statement IIThe original population was 25,000.
ExplanationStatement I gives the final count 25,760 directly, which exceeds 25,000. Statement II alone only gives the starting value.
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DS3 Medium
In a colony, children form a fixed percentage of the total population. What is the total population?
Statement I45% of the population are children.
Statement IIThere are 1,800 children in the colony.
ExplanationTotal = 1,800 × (100/45) = 4,000. Statement I gives the percentage; Statement II gives the count. Both are required. -
DS4 Medium
A city's population grows at different rates over two consecutive years. What is the population after two years?
Statement IThe initial population is 80,000.
Statement IIThe population grows by 10% in year 1 and by 5% in year 2.
ExplanationFinal = 80,000 × 1.1 × 1.05 = 92,400. Statement I gives the base; Statement II gives both annual rates.